KINEMATICS
Example
Mary swims at 3 m/s relative to still water. If she
swims directly downstream in a river which has a
uniform current of 2 m/s, what is her velocity relative
to the bank? Assume the current ows in the y
direction so 2" = 2 g j . Then Mar
Distance traveled = Ax = x2 x1 (m) ; Time traveled = At = t2 t1 (s)
Average velocity 7= AX/At (m/s) ; speed is magnitude of velocity
. . Ax dx
Instantaneous veloclty v 41:13) dt (m/s)
Average acceleration E: Av/ At (m/sz)
Instantaneous acceleration a = li
Now Mary swims directly up stream at 3 m/s
relative to still water. What is her velocity relative
to the bank?
A. 3m/sj
D. 1m/sj
iClicker question
B. 5m/sj
E. -1m/sj
c.0m/sj
S. L. Tabor Florida State University
up
C M
+3m
8.1": 6+ =
_zj+3'j=+1j
111E UEDLIUIIIUIV UF' IVIUIIUIV
Important special case of constant acceleration a
The most common case in everyday life of constant a is for objects falling
which accelerate at a = g = 9.81 m/s2 downward.
constanta=%; So v=fadt=afdt=K+at =v0+at
dx 1
V=E;
[HE UEDLKIIIIUIV U1" [WUIIUIV
EXAMPLE
You drove 164 miles from Jacksonville to Tallahassee. You drove 80
miles at 109 miles/hr [80 mi/ 109 mph = 0.73 hr], stopped for lunch for 1
hour, then drove 84 mi at 109 miles/hr [84 mi/ 109 mph = 0.77 hr]. This
took
But you were out of luck! The trooper had taken PHY2048 at FSU.
She said, That may have been you average velocity, but state law says
your instantaneous velocity cannot exceed 70 mph, and my Doppler-
effect radar gun shows your instantaneous velocity was
Unit Conversion
Lets convert these units to the standard Meter-Kilogram-Second (MKS)
units used in this course:
1 mile = 1.609 km = 1609 In; so 164 miles X (1609 m/ 1 mile) = 2.64 X 105 m
2.5 hr X (60 mink-19X (60 s/min) = 9000 s ; also 1.5 hr = 5400 s
;=